Abstract

A two-dimensional reflector with resistive-type boundary conditions and varying resistivity is considered. The incident wave is a beam emitted by a complex-source-point feed simulating an aperture source. The problem is formulated as an electromagnetic time-harmonic boundary value problem and cast into the electric field integral equation form. This is a Fredholm second kind equation that can be solved numerically in several ways. We develop a Galerkin projection scheme with entire-domain expansion functions defined on an auxiliary circle and demonstrate its advantage over a conventional moment-method solution in terms of faster convergence. Hence, larger reflectors can be computed with a higher accuracy. The results presented relate to the elliptic, parabolic, and hyperbolic profile reflectors fed by in-focus feeds. They demonstrate that a partially or fully resistive parabolic reflector is able to form a sharp main beam of the far-field pattern in the forward half-space; however, partial transparency leads to a drop in the overall directivity of emission due to the leakage of the field to the shadow half-space. This can be avoided if only small parts of the reflector near the edges are made resistive, with resisitivity increasing to the edge.

© 2009 Optical Society of America

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  1. J. M. Bendickson, E. M. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113-130 (1999).
    [CrossRef]
  2. H. Yokoi and H. Fukumuru, “Low sidelobes of paraboloidal antennas with microwave absorbers,” Electron. Commun. Jpn. 54-B, 34-49 (1971).
  3. O. Bucci and G. Franceschetti, “Rim loaded reflector antennas,” IEEE Trans. Antennas Propag. 28, 297-304 (1980).
    [CrossRef]
  4. O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981).
    [CrossRef]
  5. E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
    [CrossRef]
  6. D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995).
    [CrossRef]
  7. M. R. Barclay and W. V. T. Rusch, “Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions,” IEEE Trans. Antennas Propag. 39, 491-496 (1991).
    [CrossRef]
  8. B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).
  9. A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
    [CrossRef]
  10. T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004).
    [CrossRef]
  11. F. J. V. Hasselmann and L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677-685 (1982).
    [CrossRef]
  12. G. A. Suedan and E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521-527 (1991).
    [CrossRef]
  13. M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993).
    [CrossRef]
  14. H. Anastassiu and P. Pathak, “High-frequency analysis of Gaussian beam scattering by a two-dimensional parabolic contour of finite width,” Radio Sci. 30, 493-503 (1995).
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  20. M. Idemen and A. Büyükaksoy, “High frequency surface currents induced on a perfectly conducting cylindrical reflector,” IEEE Trans. Antennas Propag. 32, 501-507 (1984).
    [CrossRef]
  21. A. I. Nosich, “MAR in the wave-scattering and eigenvalue problems: foundations and review of solutions,” IEEE Antennas Propag. Mag. 42, 34-49 (1999).
    [CrossRef]
  22. A. I. Nosich, “Green's function--dual series approach in wave scattering from combined resonant scatterers,” in M.Hashimoto, M.Idemen and O.A.Tretyakov, eds., Analytical and Numerical Methods in Electromagnetic Wave Theory (Tokyo: Science House, 1993), pp. 419-469.
  23. T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995).
    [CrossRef]
  24. V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999).
    [CrossRef]
  25. S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000).
    [CrossRef]
  26. T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001).
    [CrossRef]
  27. A. A. Nosich and Y. V. Gandel, “Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities: E-wave case,” IEEE Trans. Antennas Propag. 57, 399-406 (2007).
    [CrossRef]
  28. A. A. Nosich, Y. V. Gandel, T. Magath, and A. Altintas, “Numerical analysis and synthesis of 2-D quasioptical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization,” J. Opt. Soc. Am. A 24, 2831-2836 (2007).
    [CrossRef]
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    [CrossRef]
  31. A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996).
    [CrossRef]
  32. A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997).
    [CrossRef]
  33. D. Colton and R. Kress, Integral Equation Method in Scattering Theory (Wiley, 1983).
  34. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).
  35. G. Bouchitte and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24, 13-26 (1989).
    [CrossRef]
  36. M. M. Lavrentyev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Analysis and Mathematical Physics (Moscow, Nauka Publ., 1980) (in Russian).
  37. A. B. Bakushinsky, “About one numerical method of solving the Fredholm first-kind integral equations,” Comput. Math. Math. Phys. 5, 744-749 (1965).

2008

2007

2005

A. Tzoulis and T. F. Eibert, “A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects,” IEEE Trans. Antennas Propag. 53, 3358-3366 (2005).
[CrossRef]

2004

A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
[CrossRef]

T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004).
[CrossRef]

2003

H.-T. Chou, P. H. Pathak, and R. J. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” Proc. Inst. Electr. Eng. 150, 177-183 (2003).

2002

C. Rieckmann, “Novel modular approach based on Gaussian beam diffraction for analysing quasi-optical multireflector antennas,” Proc. Inst. Elect. Eng. Microwaves 149, 160-167 (2002).
[CrossRef]

2001

T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[CrossRef]

2000

S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000).
[CrossRef]

1999

V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999).
[CrossRef]

A. I. Nosich, “MAR in the wave-scattering and eigenvalue problems: foundations and review of solutions,” IEEE Antennas Propag. Mag. 42, 34-49 (1999).
[CrossRef]

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

J. M. Bendickson, E. M. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113-130 (1999).
[CrossRef]

1997

A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997).
[CrossRef]

1996

A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996).
[CrossRef]

1995

T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995).
[CrossRef]

D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995).
[CrossRef]

H. Anastassiu and P. Pathak, “High-frequency analysis of Gaussian beam scattering by a two-dimensional parabolic contour of finite width,” Radio Sci. 30, 493-503 (1995).
[CrossRef]

1993

M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993).
[CrossRef]

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).

1991

G. A. Suedan and E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521-527 (1991).
[CrossRef]

M. R. Barclay and W. V. T. Rusch, “Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions,” IEEE Trans. Antennas Propag. 39, 491-496 (1991).
[CrossRef]

1989

G. Bouchitte and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24, 13-26 (1989).
[CrossRef]

1984

M. Idemen and A. Büyükaksoy, “High frequency surface currents induced on a perfectly conducting cylindrical reflector,” IEEE Trans. Antennas Propag. 32, 501-507 (1984).
[CrossRef]

1982

F. J. V. Hasselmann and L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677-685 (1982).
[CrossRef]

1981

O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981).
[CrossRef]

1980

O. Bucci and G. Franceschetti, “Rim loaded reflector antennas,” IEEE Trans. Antennas Propag. 28, 297-304 (1980).
[CrossRef]

1971

H. Yokoi and H. Fukumuru, “Low sidelobes of paraboloidal antennas with microwave absorbers,” Electron. Commun. Jpn. 54-B, 34-49 (1971).

1965

A. B. Bakushinsky, “About one numerical method of solving the Fredholm first-kind integral equations,” Comput. Math. Math. Phys. 5, 744-749 (1965).

Altintas, A.

A. A. Nosich, Y. V. Gandel, T. Magath, and A. Altintas, “Numerical analysis and synthesis of 2-D quasioptical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization,” J. Opt. Soc. Am. A 24, 2831-2836 (2007).
[CrossRef]

T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[CrossRef]

V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999).
[CrossRef]

A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997).
[CrossRef]

T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995).
[CrossRef]

Anastassiu, H.

H. Anastassiu and P. Pathak, “High-frequency analysis of Gaussian beam scattering by a two-dimensional parabolic contour of finite width,” Radio Sci. 30, 493-503 (1995).
[CrossRef]

and Altintas, A.

T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004).
[CrossRef]

S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000).
[CrossRef]

Bakushinsky, A. B.

A. B. Bakushinsky, “About one numerical method of solving the Fredholm first-kind integral equations,” Comput. Math. Math. Phys. 5, 744-749 (1965).

Barclay, M. R.

M. R. Barclay and W. V. T. Rusch, “Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions,” IEEE Trans. Antennas Propag. 39, 491-496 (1991).
[CrossRef]

Bendickson, J. M.

Bleszynski, E.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).

Bleszynski, M.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).

Boriskina, S. V.

S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000).
[CrossRef]

Bouchitte, G.

G. Bouchitte and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24, 13-26 (1989).
[CrossRef]

Brain, D. J.

B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).

Bucci, O.

O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981).
[CrossRef]

O. Bucci and G. Franceschetti, “Rim loaded reflector antennas,” IEEE Trans. Antennas Propag. 28, 297-304 (1980).
[CrossRef]

Burkholder, R. J.

H.-T. Chou, P. H. Pathak, and R. J. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” Proc. Inst. Electr. Eng. 150, 177-183 (2003).

Büyükaksoy, A.

M. Idemen and A. Büyükaksoy, “High frequency surface currents induced on a perfectly conducting cylindrical reflector,” IEEE Trans. Antennas Propag. 32, 501-507 (1984).
[CrossRef]

Cardama, A.

A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
[CrossRef]

Chou, H.-T.

H.-T. Chou, P. H. Pathak, and R. J. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” Proc. Inst. Electr. Eng. 150, 177-183 (2003).

Colton, D.

D. Colton and R. Kress, Integral Equation Method in Scattering Theory (Wiley, 1983).

Di Massa, G.

O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981).
[CrossRef]

Eibert, T. F.

A. Tzoulis and T. F. Eibert, “A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects,” IEEE Trans. Antennas Propag. 53, 3358-3366 (2005).
[CrossRef]

Felsen, L. B.

F. J. V. Hasselmann and L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677-685 (1982).
[CrossRef]

Franceschetti, G.

O. Bucci and G. Franceschetti, “Rim loaded reflector antennas,” IEEE Trans. Antennas Propag. 28, 297-304 (1980).
[CrossRef]

Fukumuru, H.

H. Yokoi and H. Fukumuru, “Low sidelobes of paraboloidal antennas with microwave absorbers,” Electron. Commun. Jpn. 54-B, 34-49 (1971).

Gandel, Y. V.

A. A. Nosich and Y. V. Gandel, “Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities: E-wave case,” IEEE Trans. Antennas Propag. 57, 399-406 (2007).
[CrossRef]

A. A. Nosich, Y. V. Gandel, T. Magath, and A. Altintas, “Numerical analysis and synthesis of 2-D quasioptical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization,” J. Opt. Soc. Am. A 24, 2831-2836 (2007).
[CrossRef]

Gaylord, T. K.

Glytsis, E. M.

Hasselmann, F. J. V.

F. J. V. Hasselmann and L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677-685 (1982).
[CrossRef]

Heldring, A.

A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
[CrossRef]

Idemen, M.

M. Idemen and A. Büyükaksoy, “High frequency surface currents induced on a perfectly conducting cylindrical reflector,” IEEE Trans. Antennas Propag. 32, 501-507 (1984).
[CrossRef]

Jaroszewicz, T.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).

Jenn, D. C.

D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995).
[CrossRef]

Jull, E. V.

G. A. Suedan and E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521-527 (1991).
[CrossRef]

Kress, R.

D. Colton and R. Kress, Integral Equation Method in Scattering Theory (Wiley, 1983).

Lavrentyev, M. M.

M. M. Lavrentyev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Analysis and Mathematical Physics (Moscow, Nauka Publ., 1980) (in Russian).

Ligthart, L. P.

A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
[CrossRef]

Magath, T.

Martin, A.

M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993).
[CrossRef]

Martinez-Burdalo, M.

M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993).
[CrossRef]

Moghaddam, M.

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

Morgan, A.

D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995).
[CrossRef]

Njoku, E. G.

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

Nosich, A. A.

A. A. Nosich, Y. V. Gandel, T. Magath, and A. Altintas, “Numerical analysis and synthesis of 2-D quasioptical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization,” J. Opt. Soc. Am. A 24, 2831-2836 (2007).
[CrossRef]

A. A. Nosich and Y. V. Gandel, “Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities: E-wave case,” IEEE Trans. Antennas Propag. 57, 399-406 (2007).
[CrossRef]

Nosich, A. I.

T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004).
[CrossRef]

T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[CrossRef]

S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000).
[CrossRef]

V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999).
[CrossRef]

A. I. Nosich, “MAR in the wave-scattering and eigenvalue problems: foundations and review of solutions,” IEEE Antennas Propag. Mag. 42, 34-49 (1999).
[CrossRef]

A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997).
[CrossRef]

A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996).
[CrossRef]

T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995).
[CrossRef]

A. I. Nosich, “Green's function--dual series approach in wave scattering from combined resonant scatterers,” in M.Hashimoto, M.Idemen and O.A.Tretyakov, eds., Analytical and Numerical Methods in Electromagnetic Wave Theory (Tokyo: Science House, 1993), pp. 419-469.

Oguzer, T.

T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004).
[CrossRef]

T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[CrossRef]

T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995).
[CrossRef]

Okuno, Y.

A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996).
[CrossRef]

Pathak, P.

H. Anastassiu and P. Pathak, “High-frequency analysis of Gaussian beam scattering by a two-dimensional parabolic contour of finite width,” Radio Sci. 30, 493-503 (1995).
[CrossRef]

Pathak, P. H.

H.-T. Chou, P. H. Pathak, and R. J. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” Proc. Inst. Electr. Eng. 150, 177-183 (2003).

Petit, R.

G. Bouchitte and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24, 13-26 (1989).
[CrossRef]

Philippakis, M.

B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).

Philippou, G. Y.

B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).

Philips, B.

B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).

Pogorzelski, R. J.

D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995).
[CrossRef]

Rahmat-Samii, Y.

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

Rieckmann, C.

C. Rieckmann, “Novel modular approach based on Gaussian beam diffraction for analysing quasi-optical multireflector antennas,” Proc. Inst. Elect. Eng. Microwaves 149, 160-167 (2002).
[CrossRef]

Rius, J. M.

A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
[CrossRef]

Romanov, V. G.

M. M. Lavrentyev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Analysis and Mathematical Physics (Moscow, Nauka Publ., 1980) (in Russian).

Rusch, W. V. T.

M. R. Barclay and W. V. T. Rusch, “Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions,” IEEE Trans. Antennas Propag. 39, 491-496 (1991).
[CrossRef]

Savarese, C.

O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981).
[CrossRef]

Senior, T. B. A.

T. B. A. Senior, “Some problems involving imperfect half-planes,” in P.L. E.Uslenghi, ed., Electromagnetic Scattering (Academic, 1978), pp. 185-219.

Sercel, J.

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

Shiraishi, T.

A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996).
[CrossRef]

Shishatskii, S. P.

M. M. Lavrentyev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Analysis and Mathematical Physics (Moscow, Nauka Publ., 1980) (in Russian).

Suedan, G. A.

G. A. Suedan and E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521-527 (1991).
[CrossRef]

Tzoulis, A.

A. Tzoulis and T. F. Eibert, “A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects,” IEEE Trans. Antennas Propag. 53, 3358-3366 (2005).
[CrossRef]

Umul, Y. Z.

Villar, R.

M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993).
[CrossRef]

Wilson, W. J.

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

Yalcin, U.

Yokoi, H.

H. Yokoi and H. Fukumuru, “Low sidelobes of paraboloidal antennas with microwave absorbers,” Electron. Commun. Jpn. 54-B, 34-49 (1971).

Yurchenko, V. B.

V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999).
[CrossRef]

A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997).
[CrossRef]

Comput. Math. Math. Phys.

A. B. Bakushinsky, “About one numerical method of solving the Fredholm first-kind integral equations,” Comput. Math. Math. Phys. 5, 744-749 (1965).

Electromagnetics

D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995).
[CrossRef]

Electron. Commun. Jpn.

H. Yokoi and H. Fukumuru, “Low sidelobes of paraboloidal antennas with microwave absorbers,” Electron. Commun. Jpn. 54-B, 34-49 (1971).

IEEE Antennas Propag. Mag.

A. I. Nosich, “MAR in the wave-scattering and eigenvalue problems: foundations and review of solutions,” IEEE Antennas Propag. Mag. 42, 34-49 (1999).
[CrossRef]

IEEE Trans. Antennas Propag.

A. A. Nosich and Y. V. Gandel, “Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities: E-wave case,” IEEE Trans. Antennas Propag. 57, 399-406 (2007).
[CrossRef]

T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995).
[CrossRef]

V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999).
[CrossRef]

S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000).
[CrossRef]

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).

A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997).
[CrossRef]

O. Bucci and G. Franceschetti, “Rim loaded reflector antennas,” IEEE Trans. Antennas Propag. 28, 297-304 (1980).
[CrossRef]

O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981).
[CrossRef]

A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004).
[CrossRef]

T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004).
[CrossRef]

F. J. V. Hasselmann and L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677-685 (1982).
[CrossRef]

G. A. Suedan and E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521-527 (1991).
[CrossRef]

M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993).
[CrossRef]

M. R. Barclay and W. V. T. Rusch, “Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions,” IEEE Trans. Antennas Propag. 39, 491-496 (1991).
[CrossRef]

A. Tzoulis and T. F. Eibert, “A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects,” IEEE Trans. Antennas Propag. 53, 3358-3366 (2005).
[CrossRef]

M. Idemen and A. Büyükaksoy, “High frequency surface currents induced on a perfectly conducting cylindrical reflector,” IEEE Trans. Antennas Propag. 32, 501-507 (1984).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Microwave Opt. Technol. Lett.

T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[CrossRef]

Proc. Inst. Elect. Eng. Microwaves

C. Rieckmann, “Novel modular approach based on Gaussian beam diffraction for analysing quasi-optical multireflector antennas,” Proc. Inst. Elect. Eng. Microwaves 149, 160-167 (2002).
[CrossRef]

Proc. Inst. Electr. Eng.

H.-T. Chou, P. H. Pathak, and R. J. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” Proc. Inst. Electr. Eng. 150, 177-183 (2003).

Radio Sci.

H. Anastassiu and P. Pathak, “High-frequency analysis of Gaussian beam scattering by a two-dimensional parabolic contour of finite width,” Radio Sci. 30, 493-503 (1995).
[CrossRef]

A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996).
[CrossRef]

G. Bouchitte and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24, 13-26 (1989).
[CrossRef]

Other

M. M. Lavrentyev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Analysis and Mathematical Physics (Moscow, Nauka Publ., 1980) (in Russian).

D. Colton and R. Kress, Integral Equation Method in Scattering Theory (Wiley, 1983).

T. B. A. Senior, “Some problems involving imperfect half-planes,” in P.L. E.Uslenghi, ed., Electromagnetic Scattering (Academic, 1978), pp. 185-219.

A. I. Nosich, “Green's function--dual series approach in wave scattering from combined resonant scatterers,” in M.Hashimoto, M.Idemen and O.A.Tretyakov, eds., Analytical and Numerical Methods in Electromagnetic Wave Theory (Tokyo: Science House, 1993), pp. 419-469.

B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).

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Figures (8)

Fig. 1
Fig. 1

Problem geometry for the finite parabolic-profile reflector. Thick dashed straight lines centered at reflector’s edges mark the corresponding tangents. Zigzag line centered at ( L , 0 ) marks the branch cut associated with the CSP source.

Fig. 2
Fig. 2

Relative error in the surface current density versus the matrix truncation number N tr for the uniformly resistive lossy reflectors with e = 1 (parabola) and k b = 3 . (a) Solid curve is for R = 0.2 Z 0 and dashed curve is for R = Z 0 , with other parameters being d = 20 λ and f d = 0.5 . (b) Solid curve is for d = 20 λ (here, the radius of the auxiliary circle is a = 22.35 λ and its center’s shift is L = 12.49 λ ) and dashed curve is for d = 40 λ (here, a = 44.71 λ and L = 25.0 λ ), with other parameters being f d = 0.5 and R = Z 0 .

Fig. 3
Fig. 3

Relative error in the far-field directivity versus the matrix truncation number N tr computed with MoM and our method for the uniformly resistive lossy (R is real-valued) and lossless (R is imaginary-valued) parabolic reflectors with d = 10 λ , f d = 0.4 , k b = 3 , and R = 0.5 Z 0 . Note that in this case the radius of the auxiliary circle is a = 9.43 λ and L = 5.56 λ .

Fig. 4
Fig. 4

Normalized radiation patterns for the uniformly resistive parabolic reflectors illuminated by in-focus CSPs. (a) Solid curve is for d = 20 λ and dashed curve is for d = 40 λ , with other parameters being f d = 0.5 , R = 0.1 Z 0 , and k b = 3 . (b) Solid curve is for R = Z 0 and dashed curve is for R = 0.1 Z 0 , other parameters being d = 40 λ , f d = 0.5 and k b = 3 . (c) Solid, dotted and dashed curves are for the CSP sources having k b = 1 , 3, and 5, respectively. Other parameters are d = 40 λ , f d = 0.5 and R = 0.1 Z 0 . As the lossless reflector patterns are very close to the lossy ones of the same R , they are not plotted here.

Fig. 5
Fig. 5

Directivity as a function of the relative focal distance f d for three values of parabolic aperture dimensions, d = 15 λ , 20 λ , and 25 λ plotted as solid, dashed, and dashed—dotted curves, respectively. Here, heavy curves are for the uniformly resistive lossless reflector case ( R = i 0.5 Z 0 ) , light ones are for the lossy case ( R = 0.5 Z 0 ) , and the CSP source with k b = 3 is located in focus.

Fig. 6
Fig. 6

Directivities as a function of absolute value of uniform resistivity for three reflectors with d = 10 λ , 20 λ , and 30 λ , plotted as solid, dashed, and dashed—dotted curves, respectively (lossy and lossless reflector case results are not distinguishable). Heavy curves are for the forward directivity and light curves are for the backward directivity.

Fig. 7
Fig. 7

Forward directivity versus the eccentricity of the conical-section-profile reflectors for different R values in lossy and lossless uniform-resistivity cases. The other parameters are d = 20 λ , f d = 0.5 , and k b = 3 .

Fig. 8
Fig. 8

Normalized radiation patterns for the PEC, uniformly resistive “nearly PEC,” and edge-loaded parabolic reflector cases. (a) Lossy and (b) lossless reflector cases, other parameters being d = 40 λ , f d = 0.5 , and k b = 3 . Also in both figures (a) and (b) the solid curve is the constant resisitivity case, the bold solid curve is the variable resisitivity case, and the dotted curve is the PEC case.

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

[ E T + ( r ) + E T ( r ) ] = 2 R ( r ) n ( r ) × [ H T + ( r ) H T ( r ) ] ,
E T + ( r ) = E T ( r ) , r = ( r , ϕ ) M ,
R diel = i Z 0 k h ( ɛ r 1 ) , R metal = 1 h σ ,
E z in ( r ) = H 0 ( 1 ) ( k r r s ) ,
r s = ( x 0 + i b cos β , y 0 + i b sin β ) .
E z sc ( r ) = i k Z 0 M J z ( r ) G ( r , r ) d l , r M ,
J z ( r ) = H T + ( r ) H T ( r ) .
R ( r ) J z ( r ) i k Z 0 M J z ( r ) G ( r , r ) d l = E z in ( r ) , r , r M .
R ( ϕ ) J ̃ z ( ϕ ) i k a Z 0 0 2 π J ̃ z ( ϕ ) G ( ϕ , ϕ ) l ( ϕ ) d ϕ = E z in ( ϕ ) ,
0 ϕ < θ ,
J ̃ z ( ϕ ) = 0 , θ < ϕ π ,
X ( ϕ ) = J ̃ z ( ϕ ) l ( ϕ ) = 2 i π Z 0 n = ( n + 1 ) 1 2 x n e in ϕ ,
E z inc ( ϕ ) = n = b n e in ϕ ,
b n = 1 2 π 0 2 π H 0 ( 1 ) ( k r ( ϕ ) r s ) e in ϕ d ϕ , r C .
H ( ϕ , ϕ ) = H 0 ( 1 ) ( k r ( ϕ ) r ( ϕ ) ) H 0 ( 1 ) [ 2 k a sin ( ϕ ϕ 2 ) ] .
H ( ϕ , ϕ ) = m , n = h n m e in ϕ e i m ϕ .
m , n = m 2 n 2 h n m 2 < .
n = ( n + 1 ) 1 2 x n e in ϕ = k a l ( ϕ ) π 2 R 0 ( ϕ ) n = [ ( n + 1 ) 1 2 x n J n ( k a ) H n ( 1 ) ( k a ) + p = h n , p ( p + 1 ) 1 2 x p ] e in ϕ + i π 2 l ( ϕ ) R 0 ( ϕ ) n = b n e in ϕ , ϕ < θ ,
n = ( n + 1 ) 1 2 x n e in ϕ = 0 , θ < ϕ π .
x m + n = A m n x n = B m , m = 0 , ± 1 , ± 2 , ,
A m n = π k a 2 ( n + 1 m + 1 ) 1 2 [ J n ( k a ) H n ( 1 ) ( k a ) Q n m + p = h n , p Q p m ] ,
B m = i π 2 ( m + 1 ) 1 2 s = b s Q s m ,
Q n m = 1 2 π θ θ l ( ϕ ) R 0 ( ϕ ) e i ( n m ) ϕ d ϕ .
E z ( r ) = [ Φ in ( ϕ ) + Φ sc ( ϕ ) ] ( 2 i π k r ) 1 2 e i k r ,
Φ in ( ϕ ) = e i k r 0 cos ( ϕ ϕ 0 ) e k b cos ( ϕ β ) ,
Φ sc ( ϕ ) = 1 2 π n = x n ( n + 1 ) 1 2 θ θ e in ϕ i k r ( ϕ ) cos ( ϕ ϕ ) d ϕ .
D forw = lim r π r E z ( r , π ) H ϕ * ( r , π ) 2 P rad ,
P rad = 1 π k Z 0 0 2 π Φ in ( ϕ ) + Φ sc ( ϕ ) 2 d ϕ .
D forw = 2 Φ in ( π ) + Φ sc ( π ) 2 k Z 0 P rad .
Δ cur ( N ) = max x n N x n N + 1 max x n N ,
Δ dir ( N ) = D forw N D forw N + 1 D forw N .

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